Skip to main content
SpringerLink
Log in

General Concepts

  • Chapter
Book cover Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications

Part of the book series: Understanding Complex Systems ((UCS))

  • 1142 Accesses

Abstract

In this chapter we introduce the general concepts dealing with the description of crowd dynamics characterized by a large number of individuals. We also define the so called panic and highlight its dynamic effects, such as the Braess’ paradox for pedestrian flows. We finally explain from the modeling point of view the reasons of the fail of the classical theory for conservation laws to attempt at the description of the arise of panic and, consequently, justify the introduction of a non-classical theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bellomo, N.: Modeling complex living systems. In: Modeling and Simulation in Science, Engineering and Technology.Birkhäuser Boston Inc., Boston (2008); A kinetic theory and stochastic game approach

    Google Scholar 

  2. Bellomo, N., Bellouquid, A.: On the modelling of vehicular traffic and crowds by kinetic theory of active particles. In: Naldi, G., Pareschi, L., Toscani, G., Bellomo, N. (eds.) Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences, Modeling and Simulation in Science, Engineering and Technology, pp. 273–296. Birkhäuser, Boston (2010)

    Google Scholar 

  3. Bellomo, N., Dogbé, C.: On the modelling crowd dynamics from scaling to hyperbolic macroscopic models. Math. Models Methods Appl. Sci. 18(suppl.), 1317–1345 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bellomo, N., Dogbe, C.: On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives. SIAM Rev. 53(3), 409–463 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Berk, R.: Collective Behavior. W. C. Brown Co. (1974)

    Google Scholar 

  6. Burlatsky, S., Atrazhev, V., Erikhman, N., Narayanan, S.: A Novel Kinetic Model to Simulate Evacuation Dynamics. In: Klingsch, W.W.F., Rogsch, C., Schadschneider, A., Schreckenberg, M. (eds.) Pedestrian and Evacuation Dynamics 2008, pp. 611–618. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Chalons, C.: Numerical Approximation of a Macroscopic Model of Pedestrian Flows. SIAM J. Sci. Comput. 29, 539–555 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chalons, C.: Transport-Equilibrium Schemes for Pedestrian Flows with Nonclassical Shocks. In: Schadschneider, A., Pöschel, T., Kühne, R., Schreckenberg, M., Wolf, D.E. (eds.) Traffic and Granular Flow 2005, pp. 347–356. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  9. Chalons, C., Goatin, P., Seguin, N.: General constrained conservation laws. Application to pedestrian flow modeling (to appear)

    Google Scholar 

  10. Colombo, R.M., Facchi, G., Maternini, G., Rosini, M.D.: On the continuum modeling of crowds. American Mathematical Society (AMS), Providence (2009)

    Google Scholar 

  11. Colombo, R.M., Goatin, P., Maternini, G., Rosini, M.D.: Macroscopic Models for Pedestrian Flows. In: Big Events and Transport: The Transportation Requirements for the Management of Large Scale Events, pp. 11–22. IUAV – TTL Research Unit (2010)

    Google Scholar 

  12. Colombo, R.M., Goatin, P., Rosini, M.D.: A macroscopic model for pedestrian flows in panic situations. In: Proceedings of the 4th Polish-Japanese Days. GAKUTO International Series. Mathematical Sciences and Applications, vol. 32, pp. 255–272 (2010)

    Google Scholar 

  13. Colombo, R.M., Goatin, P., Rosini, M.D.: Conservation laws with unilateral constraints in traffic modeling. In: Mussone, L., Crisalli, U. (eds.) Transport Management and Land-Use Effects in Presence of Unusual Demand, Atti del Convegno SIDT 2009 (June 2009)

    Google Scholar 

  14. Colombo, R.M., Rosini, M.D.: Pedestrian flows and non-classical shocks. Math. Methods Appl. Sci. 28(13), 1553–1567 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Colombo, R.M., Rosini, M.D.: Well posedness of balance laws with boundary. J. Math. Anal. Appl. 311(2), 683–702 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Colombo, R.M., Rosini, M.D.: Existence of nonclassical solutions in a Pedestrian flow model. Nonlinear Analysis: Real World Applications 10(5), 2716–2728 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Coscia, V., Canavesio, C.: First-order macroscopic modelling of human crowd dynamics. Math. Models Methods Appl. Sci. 18(suppl.), 1217–1247 (2008)

    Google Scholar 

  18. Diethelm, O.: The Nosological Position of Panic Reactions. Am. J. Psychiatry 90(6), 1295–1316 (1934)

    Google Scholar 

  19. Farkas, I., Helbing, D., Vicsek, T.: Human waves in stadiums. Phys. A 330(1-2), 18–24 (2003); Randomness and complexity (Eilat, 2003)

    Google Scholar 

  20. Helbing, D., Johansson, A., Al-Abideen, H.Z.: Dynamics of crowd disasters: An empirical study. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 75(4), 046109 (2007)

    Google Scholar 

  21. Helbing, D., Schönhof, M., Stark, H.U., Hoℓyst, J.A.: How individuals learn to take turns: emergence of alternating cooperation in a congestion game and the prisoner’s dilemma. Adv. Complex Syst. 8(1), 87–116 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Helbing, D., Siegmeier, J., Lämmer, S.: Self-organized network flows. Netw. Heterog. Media 2(2), 193–210 (2007) (electronic)

    Google Scholar 

  23. Hoogendoorn, S., Bovy, P.H.L.: Simulation of pedestrian flows by optimal control and differential games. Optimal Control Appl. Methods 24(3), 153–172 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  24. Hoogendoorn, S., Bovy, P.H.L.: Pedestrian Route-Choice and Activity Scheduling Theory and Models. Transp. Res. B (38), 169–190 (2004)

    Google Scholar 

  25. Hughes, R.L.: A continuum theory for the flow of pedestrians. Transportation Research Part B 36, 507–535 (2002)

    Article  Google Scholar 

  26. Hughes, R.L.: The flow of human crowds. Annual Review of Fluid Mechanics 35, 169–182 (2003)

    Article  ADS  Google Scholar 

  27. Johansson, A., Helbing, D., Shukla, P.K.: Specification of the social force pedestrian model by evolutionary adjustment to video tracking data. Adv. Complex Syst. 10(suppl. 2), 271–288 (2007)

    Google Scholar 

  28. Lighthill, M.J., Whitham, G.B.: On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. London. Ser. A. 229, 317–345 (1955)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. McPhail, C.: The Myth of the Madding Crowd. Walter de Gruyter, New York (1991)

    Google Scholar 

  30. Piccoli, B., Tosin, A.: Time-evolving measures and macroscopic modeling of pedestrian flow. Preprint, arXiv:0811.3383v1 (submitted)

    Google Scholar 

  31. Piccoli, B., Tosin, A.: Pedestrian flows in bounded domains with obstacles. Continuum Mechanics and Thermodynamics (21), 85–107 (2009)

    Google Scholar 

  32. Rangel-Huerta, A., Munoz-Melendez, A.: Kinetic theory of situated agents applied to pedestrian flow in a corridor. Physica A: Statistical Mechanics and its Applications 389(5), 1077–1089 (2010)

    Article  ADS  Google Scholar 

  33. Richards, P.I.: Shock waves on the highway. Operations Res. 4, 42–51 (1956)

    Article  MathSciNet  Google Scholar 

  34. Rosini, M.D.: Nonclassical interactions portrait in a macroscopic pedestrian flow model. J. Differential Equations 246(1), 408–427 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  35. Schadschneider, A., Kirchner, A., Nishinari, K.: Cellular automata simulation of collective phenomena in pedestrian dynamics. In: Interface and Transport Dynamics. Lect. Notes Comput. Sci. Eng., vol. 32, pp. 390–405. Springer, Berlin (2003)

    Chapter  Google Scholar 

  36. Smelser, N.: Theory of Collective Behavior. Free Pres, New York (1962)

    Google Scholar 

  37. Spencer, D.: Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals. The Journal of Architecture 14(3), 446–450 (2009)

    Article  Google Scholar 

  38. Sugiyama, Y., Nakayama, A.: Modeling, simulation and observations for freeway traffic and pedestrian. In: Interface and Transport Dynamics. Lect. Notes Comput. Sci. Eng., vol. 32, pp. 406–421. Springer, Berlin (2003)

    Chapter  Google Scholar 

  39. Tajima, Y., Nagatani, T.: Scaling behavior of crowd flow outside a hall. Physica A 292, 545–554 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. Takimoto, K., Nagatani, T.: Spatio-temporal distribution of escape time in evacuation process. Physica A 320, 611–621 (2003)

    Article  ADS  MATH  Google Scholar 

  41. Venuti, F., Bruno, L.: Crowd-structure interaction in lively footbridges under synchronous lateral excitation: A literature review. Physics of Life Reviews (6), 176–206 (2009) (in Press, corrected proof)

    Google Scholar 

  42. Venuti, F., Bruno, L., Bellomo, N.: Crowd dynamics on a moving platform: mathematical modelling and application to lively footbridges. Math. Comput. Modelling 45(3-4), 252–269 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  43. Yamamoto, K., Kokubo, S., Nishinari, K.: Simulation for pedestrian dynamics by real-coded cellular automata (RCA). Physica A: Statistical Mechanics and its Applications 379(2), 654–660 (2007)

    Article  ADS  Google Scholar 

  44. Yu, W., Johansson, A.: Modeling crowd turbulence by many-particle simulations. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 76(4), 046105 (2007)

    Google Scholar 

  45. Yue, H., Guan, H., Zhang, J., Shao, C.: Study on bi-direction pedestrian flow using cellular automata simulation. Physica A: Statistical Mechanics and its Applications 389(3), 527–539 (2010)

    Article  ADS  Google Scholar 

  46. Zhen, W., Mao, L., Yuan, Z.: Analysis of trample disaster and a case study – mihong bridge fatality in china in 2004. Safety Science 46(8), 1255–1270 (2008)

    Article  Google Scholar 

  47. Zheng, X., Zhong, T., Liu, M.: Modeling crowd evacuation of a building based on seven methodological approaches. Building and Environment 44(3), 437–445 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ICM, University of Warsaw, ul. Prosta 69, 00-838, Warsaw, Poland

    Massimiliano Daniele Rosini

Authors
  1. Massimiliano Daniele Rosini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Massimiliano Daniele Rosini .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 SpringerBerlin Heidelberg

About this chapter

Cite this chapter

Rosini, M.D. (2013). General Concepts. In: Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications. Understanding Complex Systems. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00155-5_15

Download citation

Publish with us

Policies and ethics

Search

Navigation